Robust output stability and input-to-output stability based on output dissipation

TL;DR

This paper extends output stability analysis to systems with inputs, using output dissipation techniques and a relaxed Barb__lat's lemma, demonstrating robustness and input-to-output stability with applications in adaptive control.

Contribution

It introduces new conditions for robust and input-to-output stability in systems with inputs, expanding output dissipation methods and applying a relaxed Barb__lat's lemma.

Findings

Extended output dissipation techniques to input systems.

Established input-to-output stability under new conditions.

Validated results in adaptive control context.

Abstract

LaSalle techniques to ensure the convergence of a given output usually fail at guaranteeing uniform convergence time, which induces robustness issues. Recent works have provided extra conditions under which a Lyapunov function that dissipates in terms of only the output guarantees this uniformity. In this paper, we extend these results to systems with inputs in order to establish either robust stability or input-to-output stability. In addition, we show that a recent relaxation of Barb__lat's lemma is also applicable to systems with inputs. The significance of the proposed results is demonstrated in the context of a recent adaptive control scheme.